Minimum Cost Layout Decomposition and Legalization for Triple Patterning Lithography

With the need of 16/11nm cells, triple patterning lithography (TPL) has been concerned in lithography industry. Basing on a new projection method for identifying conflicts, we solve the TPL layout decomposition problem in two steps. First, we formulate in this paper the TPL layout decomposition problem as a minimum cost coloring problem, and it is relaxed to a nonlinear 0-1 programming problem. Second, legalization methods are introduced to legalize a solution of the nonlinear 0-1 programming problem to a feasible one. At the legalization step, we prior utilize one-stitch insertions to eliminate conflicts. For very few independent components, a backtrack coloring algorithm is also used at this step to obtain a better relaxation coloring solution. At last, to improve scalability of our decomposition method, two graph reduction methods are adopted. We test our decomposition approach on the ISCAS-85 & 89 benchmarks. Comparisons of experimental results show that our approach achieves optimal costs better than those of state-ofthe-art decomposers. Moreover, our decomposition approach is faster than most of the decomposers on the tested benchmarks.